The fractional difference equations have been studied only recently.
In 1989, Miller and Ross began this investigations[1]}.
Some of the studies
in fractional difference equations are
due to Atici and coworkers [2]}, [3]}, Holm[4]},
and others
[5]}, [6]}.
We extend this definition to the coupled fractional difference
equations. While exploratory works on fractional equivalents
of known nonlinear maps can yield useful insights, we focus on
linear systems in this work. Linearizations of nonlinear
systems are a standard tool in difference equtions as well as
coupled difference equations. Most of analytic work in these systems
is dependent on linearization. Thus understanding linear systems and
coupled linear systems is extremely important in nonlinear
dynamics. We believe that studies in linear systems can be equally
useful in fractional difference equations.
